Accelerating Gaussian Process surrogate modeling using Compositional Kernel Learning and multi-stage sampling framework

Abstract

Surrogate modeling is becoming a popular tool to approximate computationally-expensive simulations for complex engineering problems. In practice, there are still difficulties in surrogate modeling as follows: (1) efficient learning for functional relationship of simulation models and (2) diagnostics for the surrogate model. In order to address these difficulties simultaneously, this paper proposes a new sequential surrogate modeling by integrating a Compositional Kernel Learning (CKL) method for Gaussian process into a sequential sampling strategy termed the Progressive Latin Hypercube Sampling (PLHS). The CKL enables efficient learning capability for complex response surfaces based on richly structured kernels, while the PLHS sequentially generates nested samples by maintaining desired properties for distribution. Furthermore, this sequential sampling framework allows users to monitor the diagnostics of the surrogate model and assess the stopping criteria for further sampling. In order to demonstrate useful features of the proposed method, nine test functions were assembled for numerical experiments to cover different types of problems (i.e., scale and complexity). The proposed method was evaluated with a set of surrogate modeling techniques and sampling methods in terms of performance, diagnostics and computational cost. The results show that (1) the proposed method can learn various response surfaces with fewer training samples than other methods; and (2) the proposed method only provides a reliable diagnostic measure for global accuracy over different types of problems.